Early on in the game you will find out that Zero is clearly wearing a disguise to hide his true identity. You will not find out his true identity until you are close to the end of the game. It is very obvious who he is once you reach the scene that explains it. The games story pretty much tells you straight out who he is and what his name is so there is no way this can be missed.
If you don’t want to wait then here is major SPOILER
Zeros Real Name = DELTA